What is the physical interpretation of $\oint \mathbf{A} \cdot d\mathbf{l}$? 1. The current density $\mathbf{J}$ 2. The magnetic field $\mathbf{B}$ 3. The magnetic flux $\Phi_B$ 4. It's none of the above, but is something simple and concrete 5. It has no particular physical interpretation at all Note: * CORRECT ANSWER: C

## Announcements * Final Exam: Tuesday Dec 11th * 12:45pm-2:45pm * In this room (BPS 1415) * See me for accomodations * Details on Monday

## Magnetic Dipoles <img src="./images/magfield_dipole.png" align="center" style="width: 500px";/>

The leading term in the vector potential multipole expansion involves: $\oint d\mathbf{l}'$ What is the magnitude of this integral? 1. $R$ 2. $2\pi R$ 3. 0 4. Something entirely different/it depends! Note: * CORRECT ANSWER: C

The vector potential for the dipole is: $\mathbf{A}_d = \dfrac{\mu_0}{4\pi r^2} \mathbf{m} \times \hat{\mathbf{r}}$ What is the magnitude of that cross product $|\mathbf{m} \times \hat{\mathbf{r}}|$? 1. 1 2. $m$ 3. $m r\sin\theta$ 4. $m\sin\theta$ 5. Something else? Note: Correct Answer is D

The vector potential for the dipole is: $\mathbf{A}_d = \dfrac{\mu_0}{4\pi r^2} \mathbf{m} \times \hat{\mathbf{r}}$ If the magnetic dipole moment points in the $\hat{\mathbf{z}}$ direction, what is the direction of the $\mathbf{A}_d$? 1. $\hat{\mathbf{z}}$ 2. $\hat{\mathbf{\phi}}$ 3. $\hat{\mathbf{r}}$ 4. $\hat{\mathbf{m}}$ 5. Something else? Note: Correct Answer is B

<img src="./images/magnetic_dipole_oriented.png" align="left" style="width: 300px";/> Two magnetic dipoles $m_1$ and $m_2$ (equal in magnitude) are oriented in three different ways. Which ones can produce a dipole field at large distances? 1. None of these 2. All three 3. 1 only 4. 1 and 2 only 5. 1 and 3 only Note: * CORRECT ANSWER: E

<img src="./images/magnetic_dipole_oriented.png" align="left" style="width: 300px";/> Two magnetic dipoles $m_1$ and $m_2$ (**unequal** in magnitude) are oriented in three different ways. Which ones can produce a dipole field at large distances? 1. None of these 2. All three 3. 1 only 4. 1 and 2 only 5. 1 and 3 only Note: * CORRECT ANSWER: B

## Magnets, how do they work? <img src="./images/icp.png" align="center" style="width: 700px";/> [Insane Clown Posse - Miracles](https://www.youtube.com/watch?v=_-agl0pOQfs)

## Paramagnetism & Magnetic Domains <img src="./images/magnetization.jpg" align="center" style="width: 700px";/>